Conquer

You need to build as many colony pods and military units as possible. Get some scouts (preferaby rovers) out early and quickly. Your goal is to conquer as many people as possible while they are still starting out. You should use fast rovers instead of slow infantry units for this purpose.

Technology becomes very important in a conquer game, and your research should focus mainly in the conquer area. For example, get applied physics (laser, attack 2) and nonlinear mathematics (particle impactor, attack 4) first thing, followed by doctrine: mobility (rover chassis). Your next choice should be whether to go for Synthetic Fossil Fuels (missle launcher, attack 6) or Superstring Theory (chaos gun, attack 8). Don't even bother with Superconductor (Gatling laser, attack 5), as the technologies it leads to are fairly useless until later on in the game. Synthetic fossil fuels is faster to discover, but sometimes it's better to go for superstring theory so you don't have to re-prototype. The one advantage to fossil fuels is that it leads to doctrine: air power (needlejet chassis). This technology can be practically useless on some maps, however, in which case superstring theory may be your best bet.

Another critical method of the Conquer strategy, and indeed any strategy, is to build as many colony pods as possible. Bases are what produce your armies, so many bases are necessary to have a strong army. The extent of your territory determines your bases' susceptibility to enemy attacks, as well as being the benchmark of power. Many bases = Unsurpassed power = collecting tribute from all the other factions.

The conquer strategy is even useful when you're not going for a conquer victory. If you eliminate all of the enemy bases except for one, then you can pursue transcendence unheeded. In addition, you need strong military power to achieve an economic victory, and you need a vast amount of territory and a powerful army to achieve diplomatic victory.

One element that cannot be overstressed is the reactor. The reactor increases the number of hit points you have. With a fission reactor you have 10, with a fusion reactor you have 20, quantum gives you 30, and singularity gives you 40. This means that if you have a fusion reactor while they still have fission, you have a 2 to 1 advantage over them!

The command nexus gives every base a command center (+2 morale to land units). This is an incredibly important secret project, as when two units with equal technology fight, the one with the highest morale usually wins.
The cyborg factory gives a bienhancement center (+2 morale to all at every base. When combined with the command nexus, this makes an unstoppable combination.

Blink Singularity Gravship: Graviton gun, singularity reactor, stasis generator, blink displacer, gravship chassis. Costs a ton to build but runs right through everything

Cloaked Cruiser Transport: Transport, Cruiser chassis, cloaking device, best reactor, armor (if it can be added at no cost), AAA (if the enemy uses lots of aircraft). Really useful for shipping troops without getting sunk. Alternatively, you can use a deep pressure hull instead of a cloak.

Cloaked Cruiser Transport: Same thing, but with a carrier deck. Again, you can use the submarine ability instead of a cloak.

Build

In the build strategy, you try to maximize your bases' industrial capacity and the wealth, and therefore power, of your nation.

War is one major element to be avoided. It puts a drain on your resources and forces your bases to build combat units instead of more useful facilities. While your bases should be well equipped for war, as they will be large and have many minerals, they are forced to build military units constantly instead of formers or other improvements. Sometimes, you may even want to give in if another faction demands tech or money to avoid conflict. If you are forced into conflict, your goal should be to conquer as many bases as necessary to make your opponent sign a truce.

In the build strategy, formers can be the most important unit in the game. They are how you get superior bases that can out-produce your oponent's bases. This is probably your only advantage in war, and in peace it can be a huge boon to your population and production.

Secret Projects

The Weather Paradigm can be extremely important, as your sole advantage is in having large, well-developed bases through the use of formers.
The Empath Guild makes it easier to get elected as governer, giving you that much-needed commerce bonus.
The Cloning Vats, which are only available late in the game, are the most important secret project for any strategy. In the build strategy, this project is vital to staying ahead of the other nations.

Discover

The discover strategy is less of a strategy by itself and more of a technique in accomplishing the other strategies. The purpose of the discover strategy is to get as much technology as possible, and therefore have the upper hand in conquest and in peace.

To use discover during a conquest game, the goals is to get as much technology as possible and overwhelm your opponents with superior weapons. Technology can be one of the decisive factors in any battle. In particular, being the first to discover air power can have huge advantages on certain maps. On others, initiative might be the critical factor. Either way, you need a decisive lead in technology in order to gain military strength.

Discovery during a build game has the same underlying principles, however you need to focus on a different area. You should focus on technologies offering important base facilities and terraforming advances. In particular, synthetic fossil fuels gives you fungicidal formers, which is important on games with heavy fungus or abundant mind worms. Ecological engineering lets you use advanced terraforming techniques, and all of the build techs are useful for this strategy.

Secret Projects

The supercollider and the Theory of Everything come fairly late in the game, but they are extremely important and should be placed with care.
The Merchant Exchange should be placed in a city with a large science capability.
The singularity inductor is one of the last secret projects in the game, but it can be critical in achieving transcendence.

Explore

The object of explore is to expand as much as possible and use your territory as a source of power or wealth. This too is a subset of the build or conquer strategies.

You can use the explore strategy to gain as much military strength as possible. You need to build as many colony pods as possible to snap up territory before someone else gets it. Ideally, you can isolate each faction by surrounding their territory with yours. This only works if they start near the ocean. This will limit the faction to one or two bases (until they get sea bases) and limit their early growth. You then want to conquer that faction as early as possible. You should be able to produce a large army because of all your bases. Even if you are behind in technology (which you shouldn't be because a large amount of bases can give you large amounts of technology), you can overwhelm your opponent by the sheer numbers of your army.

The explore strategy also is important as part of the build strategy. With this method, your goal is the same: Have as many bases as possible. You want to isolate other factions by surrounding them with your territory. This will stunt their growth and limit their technology and might. You should be building a lot of formers and base facilities, and all of the normal build strategies apply. The only difference is that you have to focus on expansion as well as development.

Secret Projects

The cloning vats, as i have said before, are extremely important no matter what your strategy. In the explore game, however, it is absolutely critical that you build this one before anybody else does.
The planetary transit system will give your cities a boost in early development.
The empath guild can help secure your vote in council.

Miscellaneous

Which faction should you use?

The Univesities and the Gaians are good choices to use. As I've said before, tech is one of the most important ares of the game. With a +2 research bonus, the University of Planet is a good choice. Especially with the Gaians or Peacekeepers focusing on other non-military technologies (such as Centauri techs), you usually can have impact infantry while they still have synthmetal or even scout patrols. Another good reason to get the University is that they start out with information networks. This means that you can get impact squads right after you get laser infantry, which means that you don't have to re-prototype on the higher levels.

The Stepdaughters of Gaia have the ability to capture mind worms, which is a good way to build a massive army. Find a large patch of fungus and move units around in it to find mind worms. If you try to attack a mind worm, you have a 1 in 4 chace of capturing it (The chance can be raised by researching certain techs). If you don't succeed, you just fight it normally.

The Spartans are an interesting choice. They have +2 morale, which can be extremely useful. It is especially useful in the demo, where a military-oriented strategy is required to beat the game in 100 turns. If you do enough social engineering (or build the right secret projects), then you can have units that start out as commando. If you have a monolith on the path that your units take to get to the front lines, they can become elite (with a +1 movement bonus) before they even start fighting!

Personally, I wouldn't even bother with the Hive, the Morganites, or the Peacekeepers. However, because the Peacekeepers have practically no bonuses or penalties at all, they are a good faction to try if you're a beginner and want to get a feel for the game. They are also useful in the explore or build strategy, as they get double votes in the planetary council.

I heard a very interesting strategy on the Alpha Centauri bulletin board (at the official site) concerning the Morganites. The player found the University of Planet early and allied with them. He then traded money for tech, which turned out to be very profitable for both sides. The Morganites made the money, and the UoP did the research!

To see a complete list of the pros and cons of each faction, go to the factions page.

Miscellaneous

You want to get as much technology as possible as early as possible. If I am the University, then I usually will go for Secrets of the Human Brain first thing. Especially on the higher levels, you have to get that very early to have a chance at picking up the free technology for discovering it first. If I'm another faction besides the University, then I generally focus on getting Lasers and Particle Impactors instead, as there is only a small chance of getting Secrets of the Human Brain first. Once I get Human Brain, I go straight for particle impactors then get mobility. By that time I should have mapped out most of my continent or island. If I'm on an island with nobody else there, I usually research flexibility, otherwise I start going for Superstring Theory (Chaos gun, attack 8) or Synthetic Fossil Fuels (Missle Turret, attack 6). I sometimes get Centauri Empathy (for mind worms), but I usually don't because I have very powerful weapons. If I'm playing as someone besides the University and I'm behind in tech, then I'll get Centauri Empathy, as mind worms are equally effective against any armor.

Many of the strategies in Alpha Centauri are much the same as in Civilization II. In fact, players of Civilization II will feel right at home. It is important to expand quickly and to conquer your rivals before they become too powerful. If you play on a tiny map, then sometimes you can conquer factions before they even discover Industrial Base (Gives synthmetal armor, defense 2). Some factions, such as the Gaians, generally research less military tech and more Centauri technology (such as mind worms). On the other hand, the Spartans usually have high-energy chemistry (Plasma Steel armor, defense 3) if I don't find them early enough.

"The best defense is a good offense." This famous quotation applies even more to Alpha Centauri. The only sure way to prevent an attack on your cities is to attack the other person first. In addition, this is central to the conquer strategy described above. All of the computer's resources will be focused on defending its cities, and your huge army of impact rovers (or impact infantry) will prevent the computer from launching a counterassault. As a matter of fact, I usually leave only one unit in my city to defend it from mind worms. The only time that this strategy does not apply is when you are surrounded by other factions. In that case, I usually leave two defense units in my border cities, even the ones next to factions that I have a truce with.

Another important strategy that is often overlooked is to only fight one faction at a time. This may seem obvious, but it is amazing how often it is overlooked. It is best to concentrate all of your resources on one opponent, rather than to scatter your troops and risk a counterattack. Put it this way: Would you rather be fighting two battles at half strength or one battle at full strength?

One of the frequent decisions you will have to make is between expansion and military. Die-hard Civilization II players will say that expansion is the most important strategy in the whole game. In Alpha Centuari, however, the situation is different. The most critical factor in choosing between these two strategies is the size of the map. In the tiny map, I usually found one or two cities and conquer the rest. I usually have conquered three or four cities in the time it would normally take to found them using the expansion strategy. However, this military strategy quickly falls apart on the higher levels (though I did beat the game in 83 turns on Talent once) or on larger maps. On a standard map, the largest size available in the demo, you usually need to found several cities to get a firm foothold. By the time you find another civilization, they will be large and hard to conquer. If you have several cities, you can mobilize your forces more quickly.

Do you have a strategy? Send it in and I will post it (if it is good, of course). Proper credit will be given to the author.